By dividing by [itex]\frac{P\Theta\Phi}{\rho^2sin^2 \phi}[/itex], we can isolate the theta variable and move it to the other side of the equation, this introduces a seperation constant, [itex]\mu[/itex]. We get:

I have a couple questions about this, it seems that I have a couple signs mixed up (compared to my book (Haberman)) and I don't know if I have done this entirely correctly. I greatly value your responses. Thank you!